Answer
$${\text{sin}}\theta = \frac{{12}}{{13}},{\text{ }}\cos \theta = \frac{5}{{13}},{\text{ }}\tan \theta = \frac{{12}}{5},{\text{ }}\cot \theta = \frac{5}{{12}},{\text{ }}\csc \theta = \frac{{13}}{{12}}$$
Work Step by Step
$$\eqalign{
& \theta = {\sec ^{ - 1}}2.6 \cr
& {\text{Write 2}}{\text{.6 as }}\frac{{13}}{5} \cr
& \theta = {\sec ^{ - 1}}\left( {\frac{{13}}{5}} \right) \cr
& {\text{From the triangle shown below,}} \cr
& \sec \theta = \frac{{13}}{5} \Rightarrow \theta = {\sec ^{ - 1}}\left( {\frac{{13}}{5}} \right) \cr
& {\text{Therefore,}} \cr
& {\text{sin}}\theta = \frac{{12}}{{13}} \cr
& \cos \theta = \frac{5}{{13}} \cr
& \tan \theta = \frac{{12}}{5} \cr
& \cot \theta = \frac{1}{{\tan \theta }} = \frac{5}{{12}} \cr
& \csc \theta = \frac{1}{{\sin \theta }} = \frac{{13}}{{12}} \cr} $$
